Date/Time : 30 Mar 2022 09:00
Venue : via Zoom
Speaker : Wei Kuo Chen, University of Minnesota

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https://nus-sg.zoom.us/j/81402485618?pwd=WlBSN2NhM2xXaGlTc1NhTFBqRjRIUT09

Meeting ID: 814 0248 5618
Passcode: 266695

Abstract: The Grothendieck L_p problem is defined as an optimization problem that maximizes the quadratic form of a Gaussian matrix over the unit L_p ball. The p=2 case corresponds to the top eigenvalue of the Gaussian Orthogonal Ensemble, while p=\infty this problem is known as the ground state energy of the Sherrington-Kirkpatrick mean-field spin glass model and its limit can be expressed by the famous Parisi formula. In this talk, I will describe the limit of this optimization problem for general p and discuss some results on the behavior of the near optimizers along with some open problems. This is based on a joint work with Arnab Sen.

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Date/Time : 02 Mar 2022 16:30
Venue : via Zoom
Speaker : Subhajit Goswami, Tata Institute of Fundamental Research

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https://nus-sg.zoom.us/j/86418786459?pwd=cVE2Wk5OSWthOUJtSEF5L0RzNURIdz09

Meeting ID: 864 1878 6459
Passcode: 815262

Abstract: In this talk I will give a brief introduction to Liouville first-passage percolation (LFPP) which is a model for random metric on the plane or a finite planar grid graph. It is studied primarily as a way to understand the random metric associated with Liouville quantum gravity (LQG). In short, the Liouville quantum gravity is a one parameter family of “canonical” random metrics on the plane. I will discuss a result on the estimates of the typical distance between two points and its implication for the Hausdorff dimension of the LQG distance. I will highlight how this estimate refutes a conjecture made in the physics literature about the LQG distance.

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Date/Time : 24 Feb 2022 09:00
Venue : via Zoom
Speaker : Leonard Wong, University of Toronto

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https://nus-sg.zoom.us/j/81306548290?pwd=RmRhYmVUemtRMjEvTW1EeFVkazFrdz09

Meeting ID: 813 0654 8290
Passcode: 312153

Abstract: Divergences such as Bregman and Kullback-Leibler divergences are fundamental in probability, statistics and machine learning. We begin by explaining how divergences arise naturally from the geometry of optimal transport. Then, we study a family of logarithmic costs – originally motivated by financial applications – which may be regarded as a canonical deformation of the negative dot product in Euclidean quadratic transport. It induces a logarithmic divergence which has remarkable probabilistic and geometric properties. As an application, we introduce a generalization of continuous-time mirror descent.

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Date/Time : 09 Feb 2022 16:30
Venue : via Zoom
Speaker : Marcin Lis, University of Vienna

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https://nus-sg.zoom.us/j/87181869950?pwd=L2xWTkV0SFJYUXFYbGJxQ1QyYVhSdz09

Meeting ID: 871 8186 9950
Passcode: 110158

Abstract: Using elementary methods we obtain a power-law lower bound on the two-point function of the planar XY spin model at low temperatures. This was famously first rigorously obtained by Fröhlich and Spencer and establishes a Berezinskii-Kosterlitz-Thouless phase transition in the model. Our argument relies on a new loop representation of spin correlations, a recent result of Lammers on delocalisation of integer-valued height functions, and classical correlation inequalities. This is joint work with Diederik van Engelenburg.

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Date/Time : 27 Jan 2022 09:00
Venue : via Zoom
Speaker : Promit K. Ghosal, MIT

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https://nus-sg.zoom.us/j/83355567762?pwd=UTFGTTRKQlZxbGhYaU9ZSE1CZmp2Zz09

Meeting ID: 833 5556 7762
Passcode: 947225

Abstract: The Kardar-Parisi-Zhang (KPZ) equation is a fundamental stochastic PDE related to the KPZ universality class. In this talk, we focus on how the tall peaks and deep valleys of the KPZ height function grow as time increases. In particular, we will ask what is the appropriate scaling of the peaks and valleys of the (1+1)-d KPZ equation and whether they converge to any limit under those scaling. These questions will be answered via the law of iterated logarithms and fractal dimensions of the level sets. The talk will be based on joint works with Sayan Das and Jaeyun Yi. If time permits, I will also mention an ongoing work with Jaeyun Yi for the (2+1)-d case.

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Date/Time : 19 Jan 2022 16:30
Venue : via Zoom
Speaker : Christian Webb, University of Helsinki

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https: https://nus-sg.zoom.us/j/81980150378?pwd=UDdlbHhNSDdEQmFLMUp6bHRSK2dFUT09

Meeting ID: 819 8015 0378
Passcode: 600818

Abstract: Logarithmically correlated fields are stochastic processes whose covariance has a logarithmic singularity on the diagonal. In the past few decades, it has been discovered that such objects play an important role in various probabilistic models ranging in areas ranging from number theory and random matrix theory to quantum field theory and random PDEs. In this talk, I will describe what these objects are and what kind of role they have played in various recent research questions.

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Date/Time : 12 Jan 2022 09:00
Venue : via Zoom
Speaker : Cheng Mao, Georgia Tech

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https://nus-sg.zoom.us/j/85910065038?pwd=ay9nT0hzR2ROeUs4U3d5dTBoMGNBdz09

Meeting ID: 859 1006 5038
Password: 753065

Abstract: Finding latent structures in networks is an important task in many fields of science and engineering.  For a variety of problems, the task can be formulated as inferring a latent permutation of vertices of a network from noisy data. Problems in this class are often computationally infeasible in the worst case due to the combinatorial nature of permutations, so statistical methods are essential for inference in large-scale networks. This talk will provide an overview of two problems: ranking items from comparisons and matching correlated networks. For each problem, I will introduce an average-case model and the associated task of learning a latent permutation. Then I will discuss recent development of efficient algorithms that come with theoretical guarantees.

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Date/Time : 16 Dec 2021 09:00
Venue : via Zoom
Speaker : Guillaume Remy, Columbia University

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https://nus-sg.zoom.us/j/82279401256?pwd=ZTg0M3dueXVNaUUrMzlIcTlsUUlLQT09

Meeting ID: 822 7940 1256
Passcode: 044547

Abstract: Liouville theory is a fundamental example of a conformal field theory (CFT) first introduced in physics by A. Polyakov to describe a canonical random 2d surface. In recent years it has been rigorously studied using probabilistic techniques. In this talk we will take a look at the integrable structure of Liouville CFT on a domain with boundary by proving exact formulas for its correlation functions. We will also discuss the connection with the conformal blocks of CFT which are fundamental functions determined by conformal invariance that underlie the exact solvability of CFT. Based on joint works with Morris Ang, Promit Ghosal, Xin Sun, Yi Sun and Tunan Zhu.

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Date/Time : 15 Dec 2021 09:00
Venue : via Zoom
Speaker : Souvik Dhara, MIT

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https://nus-sg.zoom.us/j/85163689192?pwd=cXdBOE9oa2NCU2tPZUFlMWZTV2s4Zz09

Meeting ID: 851 6368 9192
Passcode: 322049

Abstract: In this talk, I will discuss some recent challenges arising in the study of large and complex networks. Over the last decades, improved data collection methods have significantly increased the availability of empirical data on networks, and the study of networks has become relevant across multiple disciplines such as biology, computer science, physics, and statistics. This has stimulated enormous activity in the mathematics research community to understand (1) local and global structure of networks, (2) dynamic processes on them, and (3) algorithms to discover hidden patterns in networks. In this talk, I will discuss my research on the above three topics in the context of percolation process, graph limits, and community detection on networks.

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